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Page1
Lesson 2.3 • Finding the nth Term
Name
Period
Date
For Exercises 1–4, tell whether or not the rule is a linear function.
1.
n
1
2
3
4
5
f(n)
8
15
22
29
36
3. n
h(n)
1
!9
2
!6
3
4
n
g(n)
4.
5
3
!2
2.
9
1
2
3
4
5
14
11
8
5
2
1
2
3
4
5
!1
!"12"
0
1
""
2
n
!"32"
j(n)
For Exercises 5 and 6, complete each table.
5. n
1
2
3
4
5
6. n
6
f(n) ! 7n " 12
1
2
3
4
5
6
g(n) ! "8n " 2
For Exercises 7–9, find the function rule for each sequence. Then find the
50th term in the sequence.
7. n
f(n)
8. n
g(n)
9. n
h(n)
1
2
3
4
5
6
9
13
17
21
25
29
1
2
3
4
5
6
6
1
!4
!9
1
2
3
4
5
6
6.5
7
7.5
8
8.5
9
...
n
...
50
...
n
...
50
...
n
...
50
!14 !19
10. Find the rule for the number of tiles in the nth figure. Then find the
number of tiles in the 200th figure.
n
1
2
3
Number
of tiles
1
4
7
4
5
...
n
...
200
11. Sketch the next figure in the sequence. Then complete the table.
n
1
2
Number of
segments
and lines
2
6
Number of
regions of
the plane
Discovering Geometry Practice Your Skills
©2003 Key Curriculum Press
3
4
...
n
...
50
4
CHAPTER 2
11
Name
Class
Practice 2-1
Date
Page2
Conditional Statements
Show that each conditional is false by finding a counterexample.
1. If it is 12:00 noon, then the sun is shining.
2. If the car is full of gas, then the engine will start.
3. If a number is divisible by 3, then it is odd.
Write the converse of each conditional.
4. If you drink milk, then you will be strong.
5. If a rectangle has four sides the same length, then it is a square.
6. If you do not sleep, you will be tired.
Write the converse of each statement. If the converse is true, write true; if it
is not true, provide a counterexample.
7. If x - 4 = 22, then x = 26.
8. If ∆x∆ ! 0, then x ! 0.
9. If m2 is positive, then m is positive.
10. If y = 3, then 2y - 1 = 5.
11. If point A is in the first quadrant of a coordinate grid, then x ! 0.
12. If two lines have equal slopes, then the lines are parallel.
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13. If you are a twin, then you have a sibling.
14. Draw a Venn diagram to illustrate the statement in Exercise 13.
Answer the following questions about the given quote.
“If you like to shop, then visit the Pigeon Forge outlets in Tennessee.”
15. Identify the hypothesis and the conclusion.
16. What does the quote suggest about the Pigeon Forge outlets?
17. Write the converse of the conditional.
18. Is the converse of the conditional a true statement? Explain your
reasoning.
Answer the following questions about the billboard advertisement shown.
19. What does the billboard imply?
20. Write the advertisement slogan as a conditional statement.
Train harder,
run faster
with
SUSTAIN
21. Write the converse of the conditional statement from Exercise 20.
Geometry Chapter 2
Lesson 2-1 Practice
1
Name
Class
Date
Page3
Practice 2-2
Biconditionals and Definitions
Each conditional statement is true. Consider each converse. If the converse
is true, combine the statements and write them as a biconditional.
1. If two angles have the same measure, then they are congruent.
2. If 2x - 5 = 11, then x = 8.
3. If n = 17, then ∆n∆ = 17.
4. If a figure has eight sides, then it is an octagon.
Write the two conditional statements that make up each biconditional.
5. A whole number is a multiple of 5 if and only if its last digit is either a
0 or a 5.
6. Two lines are perpendicular if and only if they intersect to form four
right angles.
7. You live in Texas if and only if you live in the largest state in the
contiguous United States.
Explain why each of the following is not an acceptable definition.
8. An automobile is a motorized vehicle with four wheels.
9. A circle is a shape that is round.
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10. The median of a set of numbers is larger than the smallest number in
the set and smaller than the largest number in the set.
11. Cricket is a game played on a large field with a ball and a bat.
12. A rectangle is a very pleasing shape with smooth sides and very rigid
corners.
Some figures that are piggles are shown below, as are some nonpiggles.
piggles
nonpiggles
Tell whether each of the following is a piggle.
13.
2
14.
Lesson 2-2 Practice
15.
Geometry Chapter 2
Name
Class
Practice 2-3
Date
Page4
Deductive Reasoning
Use the Law of Detachment to draw a conclusion.
1. If the measures of two angles have a sum of 90°, then the angles are
complementary.
m&A + m&B = 90
2. If the football team wins on Friday night, then practice is canceled
for Monday.
The football team won by 7 points on Friday night.
3. If a triangle has one 90° angle, then the triangle is a right triangle.
In !DEF, m&E = 90.
Use the Law of Syllogism to draw a conclusion.
4. If you liked the movie, then you saw a good movie.
If you saw a good movie, then you enjoyed yourself.
5. If two lines are not parallel, then they intersect.
If two lines intersect, then they intersect at a point.
6. If you vacation at the beach, then you must like the ocean.
If you like the ocean, then you will like Florida.
If possible, use the Law of Detachment to draw a conclusion. If not possible,
write not possible.
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7. If Robbie wants to save money to buy a car, he must get a part-time job.
Robbie started a new job yesterday at a grocery store.
8. If a person lives in Omaha, then he or she lives in Nebraska.
Tamika lives in Omaha.
9. If two figures are congruent, their areas are equal.
The area of ABCD equals the area of PQRS.
Use the Law of Detachment and the Law of Syllogism to draw conclusions
from the following statements.
10. If it is raining, the temperature is greater than 32°F.
If the temperature is greater than 32°F, then it is not freezing outside.
It is raining.
11. If you live in Providence, then you live in Rhode Island.
If you live in Rhode Island, then you live in the smallest state in the
United States.
Shannon lives in Providence.
12. If it does not rain, the track team will have practice.
If the track team has practice, the team members will warm up by
jogging two miles.
It does not rain on Thursday.
Geometry Chapter 2
Lesson 2-3 Practice
3
Name
Class
Date
Page5
Practice 5-4
Inverses, Contrapositives, and Indirect Reasoning
Identify the two statements that contradict each other.
1.
I. ABCD is a trapezoid.
II. AB 6 CD
III. BC 6 AD
A
B
D
C
A
2.
I. AB ! BC
II. m!A + m!B = 80
III. "ABC is isosceles.
B
C
Write the negation of each statement.
3. The angle measure is 65.
4. Tina has her driver’s license.
5. The figure has eight sides.
6. The restaurant is not open on Sunday.
7. "ABC is not congruent to "XYZ.
8. m!Y ! 50
Write (a) the inverse and (b) the contrapositive of each statement. Give the
truth value of each.
© Pearson Education, Inc. All rights reserved.
9. If two triangles are congruent, then their corresponding angles are
congruent.
10. If you live in Toronto, then you live in Canada.
Write the first step of an indirect proof.
11. m!A = m!B
12. TUVW is a trapezoid.
13. LM intersects NO.
14. "FGH is equilateral.
15. It is sunny outside.
16. !D is not obtuse.
17. Write an indirect proof that m!A " 90.
A
C
4
B
Lesson 5-4 Practice
Geometry Chapter 5
Name
Class
Date
Page6
Practice 2-5
Proving Angles Congruent
Find the values of the variables.
1.
2.
(2x # 10)!
(3x # 40)!
(6y # 10)! (6y " 10)!
3.
4.
32!
(4z # 10)!
z!
(9x " 4)!
5.
6.
(7x " 3)!
(4y)!
65!
(4x " 1)!
(6y)!
Write true or false.
7. &1 and &2 are vertical angles.
© Pearson Education, Inc. All rights reserved.
8. &2 and &3 are supplementary angles.
9. m&1 = m&3
10. m&3 + m&4 = 180
2
1
3
4
11. m&1 + m&3 = 180
12. &4 and &2 are adjacent angles.
Write three conclusions that can be drawn from each figure.
13.
14.
15.
O
P
M
B
C
B
D
125!
N
Q
A
O
E
A
W
C
D
Geometry Chapter 2
Lesson 2-5 Practice
5
Name
Class
Date
Page7
Practice 3-1
Properties of Parallel Lines
Classify each pair of angles as alternate interior angles, same-side interior
angles, or corresponding angles.
1.
2.
1
3.
1
2
1
2
2
4.
5.
6.
1
2
1
1
2
2
Use the figure on the right to answer Exercises 7–9.
t
7. Name all pairs of corresponding angles formed by the
transversal t and lines s and c.
1 2
4 3
8. Name all pairs of alternate interior angles formed by the
transversal t and lines s and c.
s
5 6
7 8
9. Name all pairs of same-side interior angles formed by the
transversal t and lines s and c.
c
Find ml1 and then ml2. Justify each answer.
10.
11.
12.
135"
2
© Pearson Education, Inc. All rights reserved.
100"
1
1
75"
1
2
2
Algebra Find the value of x. Then find the measure of each angle.
13.
x"
(x # 26)"
14.
15.
x"
2
(7x)"
(x ! 55)"
(3x # 5)"
16. Developing Proof Supply the missing reasons in this two-column proof.
Given: a 6 b
Prove: !1 ! !3
Statements
Reasons
1. a 6 b
1. Given
2. !1 ! !2
a. 9
b. 9
c. 9
3. !2 ! !3
4. !1 ! !3
Geometry Chapter 3
a
3
2
1
Lesson 3-1 Practice
b
1
Name
Class
Date
Page8
Practice 3-2
Proving Lines Parallel
1. Developing Proof Complete the paragraph proof for the figure shown.
Given: !RQT and !QTS are supplementary.
!TSV and !SVU are supplementary.
* ) * )
Prove: QR 6 UV
Proof Because !RQT and !QTS are supplementary, !RQT and
!QTS are a. 9 angles. By the Same-Side Interior Angles Theorem,
b. 9 6 c. 9. Because !TSV and !SVU are supplementary,
* ) * !TSV
)
and !SVU are d. 9 angles. By the e. 9 Theorem, TS 6 UV .
* ) * )
* ) * )
Because QR and UV both are parallel to f. 9, QR 6 UV by
Theorem g. 9.
Q
R
T
S
U
V
Which lines or segments are parallel? Justify your answer with a theorem or
postulate.
m
!
n
3.
v
110"
70"
5. A
d
o
R
30"
6.
70"
H
30"
T
B
G
F
H
D
a
7.
96°
E
D
U
C
84°
101°
b
79°
c
I
100"
55"
A
A
C
125"
o
65"
115"
B
4.
i
d
Algebra Find the value of x for which a n t.
8.
a
a
9.
t
t
10.
(3x)"
(x # 20)"
93"
(x # 44)"
a
t
(x ! 20)"
(2x ! 10)"
11.
(x ! 30)"
a
12.
13.
(2x ! 75)"
a
80"
t
130"
70"
t
2
(x ! 20)
Lesson 3-2 Practice
t
a
(x # 35)"
(2x ! 20)"
Geometry Chapter 3
© Pearson Education, Inc. All rights reserved.
2.
LOGICREVIEWASGN#18 Writeeachstatementasabiconditional.
1.
Congruentanglesareangleswithequalmeasure.
2.
Thewholenumbersarethenonnegativeintegers.
Page9
NAME___________________________
Writethetwostatementsthatformeachbiconditional.
3.
Twolinesareparallelifandonlyiftheyarecoplanaranddonotintersect.
Eachconditionalstatementbelowistrue.Writeitsconverse.Iftheconverseisalsotrue,combine
thestatementsasabiconditional.
4.
Iftwosegmentshavethesamelength,thentheyarecongruent.
Writetheconverseofeachconditionalstatement.
5.
Ifatriangleisarighttriangle,thenithasa90°angle.
6.
Ifyoudonotwork,youdonotgetpaid.
Writeeachsentenceasaconditional.
7.
Glassobjectsarefragile.
8.
Allobtuseangleshavemeasuregreaterthan90.
9.
Goodweathermakesapicnicenjoyable.
Writetheconverseofeachconditionalstatement.Determinethetruthvaluesoftheoriginal
conditionalanditsconverse.
10. IfyoutravelfromtheUnitedStatestoKenya,thenyouhaveapassport.
11. IfyouareinIndiana,thenyouareinIndianapolis.
12. Iftwoangleshavemeasure90,thentheanglesarecongruent.
Writethenegationofeachstatement.
13. Twoanglesarecongruent.
14. Theangleisnotobtuse.
Write(a)theinverseand(b)thecontrapositiveofeachconditionalstatement.
15. Ifafigureisasquare,thenallofitsanglesarerightangles.
16. Ifafigureisarectangle,thenithasfoursides.
Write(a)theinverseand(b)thecontrapositiveofeachstatement.Givethetruthvalueofeach.
17. IfyouliveinSarasota,thenyouliveinFlorida.
18. Iffourpointsarecollinear,thentheyarecoplanar.
Writethefirststepofanindirectproof.
19. Itisrainingoutside.
20. Atleastoneangleisobtuse.
ForExercises29–32,writeaconvincingargumentthatusesindirectreasoning.
21. Freshskidmarksappearbehindagreencaratthesceneofanaccident.Showthatthedriverofthe
greencarappliedthebrakes.
22. Anobtusetrianglecannotcontainarightangle.
Page10
UsetheLawofDetachmenttodrawaconclusion.
23. IfthevolleyballteamwinsonTuesdaynight,thenpracticeiscancelledforWednesday.
Thevolleyballteamwon3setsto0onTuesdaynight.
UsetheLawofSyllogismtodrawaconclusion.
24. Ifyouvacationinthemountains,thenyoumustlikethesnow.
Ifyoulikethesnow,thenyouwilllikeColorado.
UsetheLawofDetachmentandtheLawofSyllogismtodrawconclusionsfromthefollowing
statements.
25. IfyouliveinElPaso,thenyouliveinTexas.
IfyouliveinTexas,thenyouliveinthelargeststateintheUnitedStates.
NatalialivesinElPaso.
26. Ifitdoesnotrain,thesoftballteamwillhaveagame.
Ifthesoftballteamhasagame,theteammemberswillwarmuphittingasoftball.
ItdoesnotrainonWednesday.
EXTRACREDIT
1.
Alan,Ben,andCalareseatedasshownwiththeireyesclosed.Dianeplacesahatoneachoftheir
headsfromaboxtheyknowcontains3redand2bluehats.Theyopentheireyesandlook
forward.Alansays,“IcannotdeducewhatcolorhatI’mwearing.”Hearingthat,Bensays,“Icannot
deducewhatcolorI’mwearing,either.”Calthensays,“IknowwhatcolorI’mwearing!”Howdoes
Calknowthecolorofhishat?
Page11
Find the sequence rule (function rule) for each.
1.
n
1
2
3
4
f(n)
-8
-10
-12
-14
2.
n
1
2
3
4
f(n)
10
17
24
31
3.
n
1
2
3
4
f(n)
3
1
-1
-3
4.
n
1
2
3
f(n)
1
2
4
…
n
…
35
…
n
…
20
…
n
…
80
4
5
…
n
20
8
16
Page12
Chapter 2 test review
Name___________________________ Period_____
Find the missing angles. Show work by writing angles in picture too.
Page13
Use the following conditional statement to answer questions 13-18.
“If two lines are parallel, then they are coplanar and never intersect.”
13. Write the converse of the conditional statement.
14. Are the conditional and converse true? If true, write them as a biconditional statement.
If false, give a counterexample for the false statement.
15. Write the inverse of the conditional statement.
16. Is the inverse true or false? If false, give a counterexample.
17. Write the contrapositive of the conditional statement.
18. Is the contrapositive true or false? If false, give a counterexample.
Is each statement a good definition? If not, find a counterexample.